What would stop someone from putting their property up on multiple websites?

It's a rational decision for most sellers. There's a bunch of properties listed on AirBnB, HomeAway and VRBO (latter two being owned by the same company). For buyers I'd guess existence of previous transactions and reviews is a quality signal, as opposed to a site where you can get scammed by a dishonest seller.

There's also the niche differential. VRBO & Homeaway tend to be more for vacation rental properties (not all, but that's the trend).